Mathematical Ideas with Integrated Review and Worksheets plus NEW MyLab Math with Pearson eText -- Access Card Package (Integrated Review Courses in MyLab Math and MyLab Statistics)
1st Edition
ISBN: 9780321977274
Author: Miller, Charles, Heeren, Vern, HORNSBY, John, Christopher
Publisher: PEARSON
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Chapter 15.3, Problem 24E
To determine
The advantages of Jefferson over the Adams method.
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Students have asked these similar questions
Now the city expands to cover a new district called district C. As a result, the city hires
10 new police officers to cover the new district. This brings the total number of officers
to 50. The total population of the city is shown in the table. Complete the table using
Hamilton's method to apportion the police offices for the populations after 2000. Round
all standard quotas and the divisor to 7 decimal places if needed. You can use a
spreadsheet to help you figure out an answer or calculate using a calculator.
Find the divisor. Enter your answer in the space provided below.
Divisor:
Population
2000
Initial Quotas
Final Quotas
State
Standard
Quotas
А
6,550
11,520
4,698
22,768
B
C
Total
21.)
7.) Did a new state paradox occur? Explain your answer.
Write your response below:
Suppose a nation has 5 states, with populations shown in the chart below. The
representative body had 150 seats.
Find:
the standard divisor,
the modified divisor, and
the distribution of representatives to each state.
Then complete the table. Round all standard and modified quotas to 7 decimal places if
needed.
You can use a spreadsheet to help you figure out an answer or calculate using a
calculator
Consider the Republic of Ashbury and apportion 250 seats among the five states using Huntington-Hill method. Use the population from the
table below. You can use a spreadsheet to help you figure out an answer or calculate using a calculator. Find:
● the standard divisor,
● the modified divisor, and
the distribution of representatives to each state.
●
Representative
Seats
State
A
B
C
D
E
Total
Standard
Divisor
Modified Divisor
a
Ob
Oc
Od
250
Population
1,230,520
1,230,600
3,500,230
725,000
875,500
7,561,850
Standard
Quota
Modified
Quotas
Standard divisor: 30,247.40
Modified divisor: 30,320
States: A:41, B: 41, C: 115, D:24, E:29
Standard divisor: 30,247.40
Modified divisor: 30,305
States: A:41, B: 41, C: 116, D:24, E:29
Standard divisor: 30,247.40
Modified divisor: 30,386
States: A:40, B: 41, C: 115, D:24, E:29
Standard divisor: 30,247.40
Modified divisor: 30,320
States: A:41, B: 40, C: 115, D:24, E:29
Round Round
down up
Geometric
Mean
Hill-
Huntington
Method
Chapter 15 Solutions
Mathematical Ideas with Integrated Review and Worksheets plus NEW MyLab Math with Pearson eText -- Access Card Package (Integrated Review Courses in MyLab Math and MyLab Statistics)
Ch. 15.1 - Choosing a Poster Dog by the Plurality Method A...Ch. 15.1 - Choosing a Poster Dog by the Plurality Method A...Ch. 15.1 - Choosing a Poster Dog by Alternative Methods For...Ch. 15.1 - Choosing a Poster Dog by Alternative MethodsFor...Ch. 15.1 - Observing the Effect of the Number of Candidates...Ch. 15.1 - Observing the Effect of the Number of Candidates...Ch. 15.1 - Observing the Effect of the Number of Candidates...Ch. 15.1 - Observing the Effect of the Number of Candidates...Ch. 15.1 - Observing the Effect of the Number of Candidates...Ch. 15.1 - Observing the Effect of the Number of Candidates...
Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Holding a Runoff Election One common solution to...Ch. 15.1 - Prob. 20ECh. 15.1 - Prob. 21ECh. 15.1 - Prob. 22ECh. 15.1 - Prob. 23ECh. 15.1 - Prob. 24ECh. 15.1 - Prob. 25ECh. 15.1 - Prob. 26ECh. 15.1 - Prob. 27ECh. 15.1 - The Pairwise Comparison Method Each table...Ch. 15.1 - Prob. 29ECh. 15.1 - Prob. 30ECh. 15.1 - The Borda Method Each table represents a Borda...Ch. 15.1 - Prob. 32ECh. 15.1 - Prob. 33ECh. 15.1 - Prob. 34ECh. 15.1 - Prob. 35ECh. 15.1 - Prob. 36ECh. 15.1 - The Coombs Method The Coombs method of voting is a...Ch. 15.1 - Prob. 38ECh. 15.1 - Prob. 39ECh. 15.1 - Prob. 40ECh. 15.2 - Identifying Violations of the Majority Criterion...Ch. 15.2 - Identifying Violations of the Majority Criterion...Ch. 15.2 - Identifying Violations of the Majority...Ch. 15.2 - Identifying Violations of the Majority Criterion...Ch. 15.2 - Identifying Violations of the Condorcet...Ch. 15.2 - Identifying Violations of the Condorcet Criterion...Ch. 15.2 - Identifying Violations of the Condorcet Criterion...Ch. 15.2 - Identifying Violations of the Condorcet Criterion...Ch. 15.2 - Prob. 9ECh. 15.2 - Prob. 10ECh. 15.2 - Prob. 11ECh. 15.2 - Prob. 12ECh. 15.2 - Prob. 13ECh. 15.2 - Prob. 14ECh. 15.2 - Prob. 15ECh. 15.2 - Prob. 16ECh. 15.2 - Prob. 17ECh. 15.2 - Prob. 18ECh. 15.2 - Prob. 19ECh. 15.2 - Irrelevant Alternatives in a Hare Method Election...Ch. 15.2 - 21. Explain why a violation of the majority...Ch. 15.2 - Prob. 22ECh. 15.2 - Prob. 23ECh. 15.2 - Prob. 24ECh. 15.2 - Prob. 25ECh. 15.2 - Prob. 26ECh. 15.2 - Prob. 27ECh. 15.2 - Prob. 28ECh. 15.2 - Prob. 29ECh. 15.2 - Prob. 30ECh. 15.2 - Prob. 31ECh. 15.2 - Prob. 32ECh. 15.2 - Prob. 33ECh. 15.2 - Prob. 34ECh. 15.3 - Find each quantity (to the nearest whole number)...Ch. 15.3 - Find each quantity (to the nearest whole number)...Ch. 15.3 - Find each quantity (to the nearest whole number)...Ch. 15.3 - Find each quantity (to the nearest whole number)...Ch. 15.3 - Solve each problem.
5. New Trees for Wisconsin...Ch. 15.3 - Apportioning Computers to Schools Enrollments for...Ch. 15.3 - Assigning Faculty to Courses The English...Ch. 15.3 - 8. Apportioning Sailboats to Resorts The number of...Ch. 15.3 - Prob. 9ECh. 15.3 - 10. Show that the Webster method apportionment of...Ch. 15.3 - Prob. 11ECh. 15.3 - Prob. 12ECh. 15.3 - Prob. 13ECh. 15.3 - Prob. 14ECh. 15.3 - Prob. 15ECh. 15.3 - Find the Huntington-Hill cutoff point for rounding...Ch. 15.3 - Creating a Profile of School Bus Riders Create a...Ch. 15.3 - Prob. 18ECh. 15.3 - Prob. 19ECh. 15.3 - Prob. 20ECh. 15.3 - The standard quotas rounded up to the nearest...Ch. 15.3 - Prob. 22ECh. 15.3 - Prob. 23ECh. 15.3 - Prob. 24ECh. 15.4 - Quota Rule Violations with the Jefferson Method In...Ch. 15.4 - Quota Rule Violations with the Jefferson Method In...Ch. 15.4 - Quota Rule Violations with the Jefferson Method In...Ch. 15.4 - Quota Rule Violations with the Jefferson Method In...Ch. 15.4 - Alabama Paradox with the Hamilton Method In each...Ch. 15.4 - Alabama Paradox with the Hamilton Method In each...Ch. 15.4 - Alabama Paradox with the Hamilton Method In each...Ch. 15.4 - Alabama Paradox with the Hamilton Method In each...Ch. 15.4 - Population Paradox with the Hamilton Method In...Ch. 15.4 - Population Paradox with the Hamilton Method In...Ch. 15.4 - Population Paradox with the Hamilton Method In...Ch. 15.4 - Population Paradox with the Hamilton Method In...Ch. 15.4 - New States Paradox with the Hamilton Method In...Ch. 15.4 - New States Paradox with the Hamilton Method In...Ch. 15.4 - New States Paradox with the Hamilton Method In...Ch. 15.4 - New States Paradox with the Hamilton Method In...Ch. 15.4 - Violations of the Quota Rule? For each...Ch. 15.4 - Violations of the Quota Rule? For each...Ch. 15.4 - Violations of the Quota Rule? For each...Ch. 15.4 - Prob. 20ECh. 15.4 - Prob. 21ECh. 15.4 - Prob. 22ECh. 15.4 - Prob. 23ECh. 15.4 - Prob. 24ECh. 15.4 - Prob. 25ECh. 15.4 - 26. The Jefferson and Adams methods are both...Ch. 15 - How many different complete rankings are possible...Ch. 15 - Prob. 2TCh. 15 - Prob. 3TCh. 15 - Prob. 4TCh. 15 - Prob. 5TCh. 15 - Why is the irrelevant alternatives criterion an...Ch. 15 - Prob. 7TCh. 15 - Prob. 8TCh. 15 - Prob. 9TCh. 15 - Prob. 10TCh. 15 - Prob. 11TCh. 15 - Prob. 12TCh. 15 - Prob. 13TCh. 15 - Prob. 14TCh. 15 - Prob. 15TCh. 15 - Prob. 16TCh. 15 - Prob. 17TCh. 15 - Prob. 18TCh. 15 - Prob. 19TCh. 15 - Prob. 20TCh. 15 - Prob. 21TCh. 15 - Prob. 22TCh. 15 - Prob. 23TCh. 15 - Prob. 24TCh. 15 - Prob. 25TCh. 15 - One hundred seats are to be apportioned to 4...Ch. 15 - Prob. 27TCh. 15 - Prob. 28TCh. 15 - Prob. 29TCh. 15 - Explain the Alabama paradox.Ch. 15 - Prob. 31TCh. 15 - Prob. 32T
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- Help me pleasearrow_forwardA company has four divisions with 560, 1230, 1490, and 1760 people, respectively. A total of 18 IT workers must be allocated to each division according to their size. Complete parts (a) through (d) to find the apportionment using the Hill-Huntington method. Find the standard divisor. Find the standard quota and modified standard quota for each division. Using a modified standard divisor of 275, find the modified quota for each division. Find the geometric mean for each division. Show the rounded quota (according to the Hill-Huntington method) for each division and the final apportionment of IT workers. PLEASE WATCH GRAMMAR, PUNCTUATION, AND HAVE CLEAR FORMATTING. Thank you.arrow_forwardThe Republic of Amador is composed of five states, A, B, C, D, and E. According to the country's constitution, the Congress will have 200 seats, divided among the five states according to their respective populations. State C D E Population |(in thousands) 1112 1118 1320 1515 4935 Use Adam's method with d = 50.6 to apportion the %3D 200 congressional seats for state A and E. Seats for state A = Seats for state E =arrow_forward
- Scientific Research Corporation has offices in Boston and Chicago. The number of employees at each office is shown in the following table. There are 22 vice presidents to be apportioned between the offices. Office Employees Boston Chicago 153 1220 (a) Use the Hamilton method to find each office's apportionment of vice presidents. Boston Chicago (b) The corporation opens an additional office in San Francisco with 145 employees and decides to have a total of 24 vice presidents. If the vice presidents are reapportioned using the Hamilton method, will the new states paradox occur? Explain. Yes. Boston lost a vice president and Chicago gained one. Yes. Chicago lost a vice president and Boston gained one. O Yes. Both Boston and Chicago lost a vice president. No. Both Boston and Chicago gained a vice president. O No. The number of vice presidents in Boston and Chicago remained the same.arrow_forwardConsider the apportionment of 27 projectors for a school district with four campus locations labeled A, B, C, and D. The following table shows the apportionment of the projectors using the Hamilton method. Campus A B C D Enrollment 840 1942 320 2760 Apportionment of 27 projectors 4 9 1 13 (a) If the number of projectors to be apportioned increases from 27 to 28, what will be the apportionment if the Hamilton method is used? Campus A Campus B Campus C Campus D Did the Alabama paradox occur? YesNo (b) If the number of projectors to be apportioned using the Hamilton method increases from 28 to 29, will the Alabama paradox occur? YesNoarrow_forwardConsider the apportionment of 27 projectors for a school district with four campus locations labeled A, B, C, and D. The following table shows the apportionment of the projectors using the Hamilton method. Campus A B C D Enrollment 828 1940 312 2728 Apportionmentof 27 projectors 4 9 1 13 (a) If the number of projectors to be apportioned increases from 27 to 28, what will be the apportionment if the Hamilton method is used? Campus A Campus B Campus C Campus D Did the Alabama paradox occur? YesNo (b) If the number of projectors to be apportioned using the Hamilton method increases from 28 to 29, will the Alabama paradox occur? YesNoarrow_forward
- The following table shows the number of fifth and sixth grade teachers in a school district and the number of students in each of those grades. The number of teachers for each of the grade levels was determined by using the Huntington-Hill apportionment method. The district has decided to hire a new teacher for either the fifth or sixth grade. Fifth grade Sixth grade Number of teachers 21 22 Number of students 649 730 (a) Use the apportionment principle to determine to which grade the new teacher should be assigned. O fifth grade O sixth grade (b) Use the Huntington-Hill apportionment principle to determine to which grade the new teacher should be assigned. O fifth grade O sixth grade How does this result compare with the result in part (a)? O same result O different resultarrow_forwardUse Huntington-Hill's method of apportionment to solve the following problems. 3 Suppose a nation has 4 states, with populations shown in the chart below. The representative body had 80 seats 7 Find the standard divisor and the distribution of representatives to each state using the Huntington-Hill method of apportionment. Round the standard quotas to 7 decimal places if needed. You can use a spreadsheet to help you figure out an answer or calculate using a calculator.arrow_forwardA company has four divisions with 560, 1230, 1490, and 1760 people, respectively. A total of 18 IT workers must be allocated to each division according to their size. find the apportionment using the Hill-Huntington method. a. find standard divisor b. Find the standard quota and modified standard quota for each division.arrow_forward
- Consider the apportionment of 27 projectors for a school district with four campus locations labeled A, B, C, and D. The following table shows the apportionment of the projectors using the Hamilton method. Campus A B D Enrollment 824 1946 322 2738 Apportionment of 27 projectors 4 9 13 (a) If the number of projectors to be apportioned increases from 27 to 28, what willI be the apportionment if the Hamilton method is used? Campus A Campus B Campus C Campus D (No Response) (No Response) (No Response) (No Response) Did the Alabama paradox occur? O Yes O No (b) If the number of projectors to be apportioned using the Hamilton method increases from 28 to 29, will the Alabama paradox occur? O Yes O Noarrow_forwardAlabama Paradox There are 3 states and 20 seats. In 20 years, the number of seats was increased to 21. Suppose the years are 2000 and 2020. 1.) Complete the table using Hamilton's method to apportion the 20 seats for the populations after 2000 and the 21 seats after 2020. Round all standard quotas and the divisor to 7 decimal places if needed. You can use a spreadsheet to help you figure out an answer or calculate using a calculator. Fill in every cell. 20 seats 21 seats State Population 2000 Standard Initial Final Standard Initial Final Quotas Quotas Quotas Quotas Quotas Quotas A 5,222 В 9,677 15,821 30,720 C Total 2.) What are the two divisors? Enter your answer in the space provided below. Divisor for 20 seats: Divisor for 21 seats: 3.) Did an Alabama paradox occur? Explain your answer. Write your response below:arrow_forwardThere are 3 states and 20 seats. In 20 years, the number of seats was increased to 21. Suppose the years are 2000 and 2020. 1.) Complete the table using Hamilton's method to apportion the 20 seats for the populations after 2000 and the 21 seats after 2020. Round all standard quotas and the divisor to 7 decimal places if needed. You can use a spreadsheet to help you figure out an answer or calculate using a calculator. Fill in every cell. 20 seats 21 seats State Population 2000 Standard Initial Final Standard Initial Final Quotas Quotas Quotas Quotas Quotas Quotas 5,222 9,677 15,821 30,720 А B C Total 2.) What are the two divisors? Enter your answer in the space provided below. Divisor for 20 seats: Divisor for 21 seats:arrow_forward
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